Self-Weighted Euler $k$-Means Clustering

Clustering is used widely in various kinds of signal processing tasks, in which
$k$
-means is warmly welcomed by the researchers due to its efficiency and simplicity. Nevertheless, it fails to process non-spherical clusters which are common data distribution. As a variant of
$k$
-means, kernel
$k$
-means uses a kernel trick to map the raw data into a feature space to better describe the data with improved clustering performance. But the algorithms still have a lot of shortcomings in the application of signal processing: 1) Not all features contain a wealth of useful information, so all dimensions of features cannot be treated equally; 2) The use of high dimensional features for clustering exceedingly increases computational complexity with negligible improvement of clustering performance. To solve the problems, we propose a self-weighted Euler
$k$
-means (SWEKM) model, which can adaptively identify the importance of different features, perfectly integrating clustering and feature selection into a joint framework. Moreover, Euler kernel is adopted in SWEKM, which is capable of suppressing the interference of noisy points and outliers with comparable computational complexity. Extensive experiments on datasets from the UCI database show that the SWEKM outperforms the state-of-the-art kernel
$k$
-means for clustering-based signal processing tasks.